The Harnack inequality for second-order elliptic equations with divergence-free drifts
type: Item
instance of: scholarly article
title: The Harnack inequality for second-order elliptic equations with divergence-free drifts
zbMATH Open document ID: 1308.35039
author: Mihaela Ignatova
author: Igor Kukavica
author: Lenya Ryzhik
published in: Communications in Mathematical Sciences
publication date: 2014-11-18T00:00:00Z
review text: The authors consider the elliptic equation \[ - \Delta u + b\cdot \nabla u +au =0 \] assuming \(b\) a divergence free vector field. Such kind of equation was studied by Stampacchia without the divergence free condition. Assuming the free boundary condition, it was studied by several authors, among them we quote Nazarov, Uralt'seva, Friedlander, Vicol, Seregin, Silvestre, Sverak and Zlatos. In this very interesting paper the authors establish a Harnack type inequality and a one side Liouville estimate under suitable assumptions of integrability on the coefficients \(a\) and \(b\).
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B53
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 6370327
zbMATH Keywords: drift-diffusion equations, divergence free condition
MaRDI profile type: Publication
DOI: 10.4310/CMS.2014.V12.N4.A4
description: scientific article; zbMATH DE number 6370327